Final answer:
The equilibrium output in a Keynesian economy is calculated by equating aggregate expenditure (AE) to real GDP (Y), which includes factors like consumption, investment, and government spending. An increase in government spending affects the short-run output and price level, with potential long-run adjustments returning the economy back to its potential output.
Step-by-step explanation:
Finding Keynesian Equilibrium
Understanding a Keynesian economy involves analyzing consumption (C), investment (I), government spending (G), taxes (T), and sometimes exports (X) and imports (M), as well as other components like the real interest rate and the price level. To find the equilibrium output, we look for the level of real GDP (Y) where planned aggregate expenditure equals real GDP. This typically occurs where the aggregate expenditure schedule intersects the 45-degree line on a Keynesian Cross Diagram.
Consider an economy with the following assumptions:
Autonomous consumption (without income) is $20.
Taxes are 0.2 of real GDP (T = 0.2Y).
The marginal propensity to save of after-tax income is 0.1.
Investment level is $70.
Government spending is $80.
Exports are $50.
Imports are 0.2 of after-tax income.
To find the equilibrium output (Ye), we solve for Y in the following aggregate expenditure function:
AE = C + I + G + X - M
Given the values mentioned, and assuming a closed economy (no exports or imports), we can calculate the equilibrium output using the consumption function plus investment and government spending.
C = 20 + 0.8(Y - 0.2Y) = 400 + 0.64Y
AE = C + I + G
AE = (400 + 0.64Y) + 70 + 80
To find Ye, we equate AE to Y:
Y = 400 + 0.64Y + 150
This results in a simple algebraic problem where we solve for Y, and subsequently use it to calculate other economic variables such as the real interest rate and price level.
When government spending changes, the short-run and long-run effects may differ. In the short run, an increase in government spending increases aggregate demand, potentially increasing output and the price level. However, in the long run, the economy tends to return to its potential output level, and prices adjust fully.